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C2×(C5⋊D5)⋊(C13⋊C3) #16839128

order3900
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×(C5⋊D5)⋊(C13⋊C3)
unambiguous semidirect product(C2×C5⋊D5)⋊(C13⋊C3)

Splittings

Fitting, socleC2×C52×C13 ⋊ C2×C3
derived, HallC52×C13 ⋊ C22×C3
HallC2×C13×C5⋊D5 ⋊ C3
HallC13⋊(C52⋊C3) ⋊ C22
HallC2×C5⋊D5 ⋊ C13⋊C3
SylowC52 ⋊ C22×C13⋊C3
SylowC13 ⋊ C2×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2(C5⋊D5)⋊(C13⋊C3)
commutator, cosocle, hypocenterC52×C13C22×C3
FrattiniC1G
Fitting, socleC2×C52×C13C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 390

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13⋊C3×(C5⋊D5)⋊C3, D3×(C5⋊D5)⋊(C13⋊C3), C2×C3×(C5⋊D5)⋊(C13⋊C3), …
maximal normal subgroup ofC2×C13⋊C3×(C5⋊D5)⋊C3, C2×C3×(C5⋊D5)⋊(C13⋊C3), C2×C7×(C5⋊D5)⋊(C13⋊C3)
maximal quotient ofC2×(C5⋊D5)⋊(C13⋊C9), D3×(C5⋊D5)⋊(C13⋊C3), C2×C3×(C5⋊D5)⋊(C13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3900, 136);